Troubleshooting Bayesian cognitive models: A tutorial with matstanlib

Using Bayesian methods to apply computational models of cognitive processes, or Bayesian cognitive modeling, is an important new trend in psychological research. The rise of Bayesian cognitive modeling has been accelerated by the introduction of software such as Stan and PyMC3 that efficiently automates the Markov chain Monte Carlo (MCMC) sampling used for Bayesian model fitting. Unfortunately, Bayesian cognitive models can struggle to pass the computational checks required of all Bayesian models. If any failures are left undetected, inferences about cognition based on model output may be biased or incorrect. As such, Bayesian cognitive models almost always require troubleshooting before being used for inference. Here, we present a deep treatment of the diagnostic checks and procedures that are critical for effective troubleshooting, but are often left underspecified by tutorial papers. After a conceptual introduction to Bayesian cognitive modeling and MCMC sampling, we outline the diagnostic metrics, procedures, and plots necessary to identify problems in model output with an emphasis on how these requirements have recently been improved. Throughout, we explain how the most commonly encountered problems may be remedied with specific, practical solutions. We also introduce matstanlib, our MATLAB modeling support library, and demonstrate how it facilitates troubleshooting of an example hierarchical Bayesian model of reinforcement learning implemented in Stan. With this comprehensive guide to techniques for detecting, identifying, and overcoming problems in fitting Bayesian cognitive models, psychologists across subfields can more confidently build and use Bayesian cognitive models.All code is freely available from github.com/baribault/matstanlib.

Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

Proteins are found in all living organisms and constitute a large group of macromolecules with many functions. Proteins achieve their operations by adopting distinct three-dimensional structures encoded within the sequence of the constituent amino acids in one or more polypeptides. New, more flexible distributions are proposed for the MCMC sampling method for predicting protein 3D structures by applying a Möbius transformation to the bivariate von Mises distribution. In addition to this, sine-skewed versions of the proposed models are introduced to meet the increasing demand for modelling asymmetric toroidal data. Interestingly, the marginals of the new models lead to new multimodal circular distributions. We analysed three big datasets consisting of bivariate information about protein domains to illustrate the efficiency and behaviour of the proposed models. These newly proposed models outperformed mixtures of well-known models for modelling toroidal data. A simulation study was carried out to find the best method for generating samples from the proposed models. Our results shed new light on proposal distributions in the MCMC sampling method for predicting the protein structure environment.

Identifying Norms from Observation Using MCMC Sampling

To promote efficient interactions in dynamic and multi-agent systems, there is much interest in techniques that allow agents to represent and reason about social norms that govern agent interactions. Much of this work assumes that norms are provided to agents, but some work has investigated how agents can identify the norms present in a society through observation and experience. However, the norm-identification techniques proposed in the literature often depend on a very specific and domain-specific representation of norms, or require that the possible norms can be enumerated in advance. This paper investigates the problem of identifying norm candidates from a normative language expressed as a probabilistic context-free grammar, using Markov Chain Monte Carlo (MCMC) search. We apply our technique to a simulated robot manipulator task and show that it allows effective identification of norms from observation.

An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture

We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $$d^{-o_d(1)}$$ d - o d ( 1 ) . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $$d^{-1/4}$$ d - 1 / 4 . Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain’s slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concave measures and better mixing time bounds for MCMC sampling algorithms on log-concave measures.

Scalable Fully Bayesian Gaussian Process Modeling and Calibration with Adaptive Sequential Monte Carlo for Industrial Applications

Gaussian Process (GP) regression or kriging has been extensively applied in the engineering literature for the purposes of building a cheap-to-evaluate surrogate, within the contexts of multi-fidelity modeling, model calibration and design optimization. With the ongoing automation of manufacturing and industrial practices as a part of Industry 4.0, there has been greater need for advancing GP regression techniques to handle challenges such as high input dimensionality, data paucity or big data problems, these consist primarily of proposing efficient design of experiments, optimal data acquisition strategies, and other mathematical tricks. In this work, our attention is focused on the challenges of efficiently training a GP model, which, to the authors opinion, has attracted very little attention and is to-date, poorly addressed. The performance of widely used training approaches such as maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) sampling can deteriorate significantly in high dimensional and big data problems and can lead to cost deficient implementations of critical importance to many industrial applications. Here, we compare an Adaptive Sequential Monte Carlo (ASMC) sampling algorithm to classic MCMC sampling strategies and we demonstrate the effectiveness of our implementation on several mathematical problems and challenging industry applications of varying complexity. The computational time savings of our ASMC approach manifest in large-scale problems helping us to push the boundary of GP regression applicability and scalability in various domain of Industry 4.0, including but not limited to design automation, design engineering, predictive maintenance, and supply chain manufacturing.

Applying Knowledge Inference on Event-Conjunction for Automatic Control in Smart Building

Smart building, one of IoT-based emerging applications is where energy-efficiency, human comfort, automation, security could be managed even better. However, at the current stage, a unified and practical framework for knowledge inference inside the smart building is still lacking. In this paper, we present a practical proposal of knowledge extraction on event-conjunction for automatic control in smart buildings. The proposal consists of a unified API design, ontology model, inference engine for knowledge extraction. Two types of models: finite state machine(FSMs) and bayesian network (BN) have been used for capturing the state transition and sensor data fusion. In particular, to solve the problem that the size of time interval observations between two correlated events was too small to be approximated for estimation, we utilized the Markov Chain Monte Carlo (MCMC) sampling method to optimize the sampling on time intervals. The proposal has been put into use in a real smart building environment. 78-days data collection of the light states and elevator states has been conducted for evaluation. Several events have been inferred in the evaluation, such as room occupancy, elevator moving, as well as the event conjunction of both. The inference on the users’ waiting time of elevator-using revealed the potentials and effectiveness of the automatic control on the elevator.

Optimal scheduling of regional integrated energy system considering multiple uncertainties

Integrated energy system (IES) is an effective way to realize the efficient utilization of energy. Under the deregulated electricity market, IES operator gains profits by providing customers with energy service, including electricity, heat or cooling energy. With the deepening of market reform, higher penetration rate of renewable energy, economic risks embed in the IES. Based on this, an optimal scheduling model of regional IES considering uncertainties is proposed, aiming at maximizing the profits. Scenario analysis method has been adopted to model the uncertainties: Markov-Chain-Monte-Carlo (MCMC) sampling method, which has a better performance in fitting the probability distribution, is utilized to generate scenarios; K-means clustering method is applied to narrow down the sampling sets. By replacing the parameters in the deterministic model with the sampling sets, a series of optimal results can be achieved. The case study shows that the cooling storage tank can improve the economic benefits about 4.97% by converting electricity to cooling energy at lower price period and releasing energy at peak hours. Besides, through the proposed optimization model, operators can have a straight understanding of the venture brought by the uncertainties and a more reliable scheduling result is formed for reference.

BiTSC2: Bayesian inference of Tumor clonal Tree by joint analysis of Single-Cell SNV and CNA data

The rapid development of single-cell DNA sequencing (scDNA-seq) technology has greatly enhanced the resolution of tumor cell profiling, providing an unprecedented perspective in characterizing intra-tumoral heterogeneity and understanding tumor progression and metastasis. However, prominent algorithms for constructing tumor phylogeny based on scDNA-seq data usually only take single nucleotide variations (SNVs) as markers, failing to consider the effect caused by copy number alterations (CNAs). Here, we propose BiTSC2, Bayesian inference of Tumor clonal Tree by joint analysis of Single-Cell SNV and CNA data. BiTSC2 takes raw reads from scDNA-seq as input, accounts for sequencing errors, models dropout rate and assigns single cells into subclones. By applying Markov Chain Monte Carlo (MCMC) sampling, BiTSC2 can simultaneously estimate the subclonal scCNA and scSNV genotype matrices, sub-clonal assignments and tumor subclonal evolutionary tree. In comparison with existing methods on synthetic and real tumor data, BiTSC2 shows high accuracy in genotype recovery and sub-clonal assignment. BiTSC2 also performs robustly in dealing with scDNA-seq data with low sequencing depth and variant dropout rate.